Exact source, with stable line anchors. Download the unchanged bibliography file.
@article{Andrasfai1986,
title = {R\'ozsa ({R}osa) {P}\'eter},
author = {Andr\'asfai, B\'ela},
journal = {Periodica Polytechnica Electrical Engineering},
volume = {30},
number = {2-3},
pages = {139--145},
year = {1986},
url = {http://www.pp.bme.hu/ee/article/view/4651}
}
@misc{Aspray1984,
author = {Aspray, William},
title = {The {P}rinceton Mathematics Community in the 1930s:
{A}lonzo {C}hurch},
year = 1984,
note = {Interview},
url =
{http://www.princeton.edu/mudd/finding_aids/mathoral/pmc05.htm}
}
@book{Baaz2011,
title = {Kurt {G}\"odel and the Foundations of Mathematics:
Horizons of Truth},
author = {Baaz, Matthias and Papadimitriou, Christos H. and
Putnam, Hilary W. and Scott, Dana S. and Harper Jr.,
Charles L.},
year = 2011,
publisher = {Cambridge University Press},
address = {Cambridge}
}
@article{bailey2006,
Author = {Bailey, Ellen},
Journal = {R\'ozsa P\'eter},
Title = {R\'ozsa {P}\'eter},
URL =
{http://search.ebscohost.com/login.aspx?direct=true&db=sch&AN=20916042&site=ehost-live},
Year = {2006},
}
@Article{ButtonLT1,
Author = {Button, Tim},
Journal = {The Bulletin of Symbolic Logic},
Year = {2021},
Title = {Level Theory, Part~1: Axiomatizing the Bare Idea of a Cumulative Hierarchy of Sets},
volume = {27},
number = {4},
pages = {436-460}
}
@Article{Church1936,
author = {Alonzo Church},
title = {A note on the {E}ntscheidungsproblem},
journal = {The Journal of Symbolic Logic},
year = 1936,
volume = 1,
pages = {40--41}
}
@Article{Church1936a,
title = {An Unsolvable Problem of Elementary Number Theory},
author = {Alonzo Church},
journal = {American Journal of Mathematics},
Volume = 58,
year = 1936,
pages = {345--363}
}
@misc{Csicsery2016,
author = {Csicsery, George},
title = {Zala Films: {J}ulia {R}obinson and {H}ilbert's Tenth Problem},
year = 2016,
url = {http://www.zalafilms.com/films/juliarobinson.html}
}
@book{Dauben1990,
title = {{G}eorg {C}antor: {H}is {M}athematics and
{P}hilosophy of the {I}nfinite},
author = {Dauben, Joseph},
year = 1990,
publisher = {Princeton University Press},
address = {Princeton}
}
@article{Dauben2004,
title = {{G}eorg {C}antor and the Battle for Transfinite Set
Theory},
author = {Dauben, Joseph},
year = 2004,
journal = {Journal of the ACMS},
volume = 1,
pages = {1--17}
}
@article{DavisPutnamRobinson1961,
URL = {http://www.jstor.org/stable/1970289},
author = {Martin Davis and Hilary Putnam and Julia Robinson},
journal = {Annals of Mathematics},
number = {3},
pages = {425-436},
title = {The Decision Problem for Exponential {D}iophantine
Equations},
volume = {74},
year = {1961}
}
@book{Dawson1997,
title = {Logical Dilemmas: The Life and Work of Kurt
{G}\"odel},
author = {John Dawson, Jr.},
year = 1997,
publisher = {CRC Press},
address = {Boca Raton}
}
@book{Dick1981,
title = {Emmy {N}oether 1882--1935},
author = {Dick, Auguste},
year = 1981,
publisher = {Birkh\"auser},
address = {Boston}
}
@misc{Duncan2015,
author = {Duncan, Arlene},
title = {The {B}ertrand {R}ussell {R}esearch {C}entre},
year = 2015,
url = {http://russell.mcmaster.ca/}
}
@book{Ebbinghaus2010,
title = {Ernst Zermelo. Collected Works},
volume = 1,
author = {Ebbinghaus, Heinz-Dieter and Fraser, Craig G. and
Kanamori, Akihiro},
year = 2010,
publisher = {Springer-Verlag},
address = {Berlin}
}
@book{Ebbinghaus2013,
title = {Ernst Zermelo: Collected Works},
volume = 2,
author = {Ebbinghaus, Heinz-Dieter and Kanamori, Akihiro},
year = 2013,
publisher = {Springer-Verlag},
address = {Berlin}
}
@book{Ebbinghaus2015,
title = {Ernst {Z}ermelo: {A}n {A}pproach to his {L}ife and
{W}ork},
author = {Ebbinghaus, Heinz-Dieter},
year = 2015,
publisher = {Springer-Verlag},
address = {Berlin}
}
@incollection{EndertonND,
title = {{A}lonzo {C}hurch: {L}ife and {W}ork},
author = {Herbert B. Enderton},
editor = {Tyler Burge and Herbert B. Enderton},
booktitle = {The Collected Works of {A}lonzo {C}hurch},
publisher = {MIT Press},
year = {2019},
address = {Cambridge, MA}
}
@article{Feferman1994,
author = {Feferman, Solomon},
year = 1994,
title = {{J}ulia {B}owman {R}obinson 1919--1985},
journal = {Biographical Memoirs of the National Academy of
Sciences},
volume = 63,
pages = {1--28},
publisher = {National Academies Press},
url =
{http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/robinson-julia.pdf}
}
@book{Feferman2004,
title = {Alfred Tarski: Life and Logic},
author = {Feferman, Anita and Feferman, Solomon},
year = 2004,
publisher = {Cambridge University Press},
address = {Cambridge}
}
@misc{Frey2015,
author = {Frey, Holly and Wilson, Tracy V.},
title = {Stuff you Missed in History Class: {E}mmy
{N}oether, Mathematics Trailblazer},
year = 2015,
note = {Podcast audio},
url =
{https://www.iheart.com/podcast/stuff-you-missed-in-history-cl-21124503/episode/emmy-noether-mathematics-trailblazer-30207491/}
}
@Article{Gentzen1935a,
author = {Gerhard Gentzen},
year = 1935,
title = {Untersuchungen \"uber das logische {S}chlie\ss en
{I}},
journal = {Mathe\-mati\-sche Zeit\-schrift},
volume = 39,
issue = 1,
pages = {176--210},
note = {{E}nglish translation in \cite{Gentzen1969},
pp.~68--131},
doi = {10.1007/BF01201353}
}
@Article{Gentzen1935b,
author = {Gerhard Gentzen},
year = 1935,
title = {Untersuchungen \"uber das logische {S}chlie\ss en
{II}},
journal = {Mathe\-mati\-sche Zeit\-schrift},
volume = 39,
issue = 1,
pages = {176--210, 405--431},
note = {{E}nglish translation in \cite{Gentzen1969},
pp.~68--131},
doi = {10.1007/BF01201363}
}
@Book{Gentzen1969,
author = {Szabo, Manfred E.},
year = 1969,
title = {The Collected Papers of {G}erhard {G}entzen},
booktitle = {The Collected Papers of {G}erhard {G}entzen},
publisher = {North-Holland},
address = {Amsterdam}
}
@PHDTHESIS{Godel1929,
author = {Kurt G\"odel},
year = 1929,
title = {{\"U}ber die {V}ollst\"andigkeit des
{L}ogikkalk\"uls [{O}n the Completeness of the
Calculus of Logic]},
note = {Reprinted and translated in \cite{Godel1986},
pp.~60--101},
school = {Universit{\"{a}}t Wien},
type = {Dissertation}
}
@Article{Godel1931,
author = {Kurt G{\"{o}}del},
title = {\"Uber formal unentscheidbare {S}\"atze der
\emph{{P}rincipia {M}athematica} und verwandter
{S}ysteme {I} [{O}n Formally Undecidable
Propositions of \emph{{P}rincipia {M}athematica} and
Related Systems~{I}]},
journal = {Monatshefte f\"ur Mathematik und Physik},
year = 1931,
volume = 38,
pages = {173--198},
note = {Reprinted and translated in \cite{Godel1986},
pp.~144--195},
doi = {10.1007/BF01700692}
}
@Book{Godel1986,
title = {Kurt G\"odel: Collected Works. Vol. 1:
Publications 1929--1936},
author = {Feferman, Solomon and Dawson Jr., John W. and
Kleene, Stephen C. and Moore, Gregory H. and
Solovay, Robert M. and van Heijenoort, Jean},
year = 1986,
publisher = {Oxford University Press},
address = {Oxford}
}
@Book{Godel1990,
title = {Kurt G\"odel: Collected Works. Vol. 2:
Publications 1938--1974},
author = {Feferman, Solomon and Dawson Jr., John W. and
Kleene, Stephen C. and Moore, Gregory H. and
Solovay, Robert M. and van Heijenoort, Jean},
year = 1990,
publisher = {Oxford University Press},
address = {Oxford}
}
@article{Grattan-Guinness1971,
title = {Towards a Biography of {G}eorg {C}antor},
author = {Grattan-Guinness, Ivor},
journal = {Annals of Science},
volume = 27,
number = 4,
pages = {345--391},
year = 1971,
}
@book{Heck2012,
author = {Richard Kimberly Heck},
title = {Reading Frege's Grundgesetze},
publisher = {Oxford University Press},
year = {2012},
address = {Oxford}
}
@book{Hodges2014,
title = {Alan Turing: The Enigma},
author = {Hodges, Andrew},
year = 2014,
publisher = {Vintage},
address = {London}
}
@misc{Imitation2014,
author = {Morten Tyldum},
title = {The Imitation Game},
year = 2014,
note = {Motion picture}
}
@misc{Irvine2015,
author = {Irvine, Andrew David},
title = {Sound Clips of {B}ertrand {R}ussell Speaking},
year = 2015,
url =
{http://plato.stanford.edu/entries/russell/russell-soundclips.html}
}
@Article{Kratzer1981,
author = "Kratzer, Angelika",
title = "Partition and revision: The semantics of
counterfactuals",
journal = "Journal of Philosophical Logic",
year = 1981,
volume = 10,
number = 2,
pages = "201--216",
doi = "10.1007/BF00248849"
}
@misc{LibriVoxND,
author = {LibriVox},
title = {Bertrand {R}ussell},
year = {n.d.},
note = {Collection of public domain audiobooks},
url =
{https://librivox.org/author/1508?primary_key=1508&search_category=author&search_page=1&search_form=get_results}
}
@misc{Linsenmayer2014,
author = {Linsenmayer, Mark},
title = {The Partially Examined Life: {G}\"odel on Math},
year = 2014,
note = {Podcast audio},
url =
{http://www.partiallyexaminedlife.com/2014/06/16/ep95-godel/}
}
@misc{MacFarlane2015,
author = {MacFarlane, John},
title = {Alonzo {C}hurch's {JSL} Reviews},
year = 2015,
url = {http://johnmacfarlane.net/church.html}
}
@Article{Maddy1988a,
Author = {Penelope Maddy},
Title = {Believing the Axioms~{I}},
Journal = {The Journal of Symbolic Logic},
Year = {1988},
Volume = {53},
Number = {2},
Pages = {481--511}}
@Article{Maddy1988b,
Author = {Penelope Maddy},
Title = {Believing the Axioms~{II}},
Journal = {The Journal of Symbolic Logic},
Year = {1988},
Volume = {53},
Number = {3},
Pages = {736--64}}
@book{Magnus2021,
title = {Forall {\emph{x}}: {{Calgary}}. {{An}} Introduction to Formal Logic},
author = {Magnus, P. D. and Button, Tim and Loftis, J. Robert and {Thomas-Bolduc}, Aaron and Trueman, Robert and Zach, Richard},
year = {2021},
edition = {F21},
publisher = {{Open Logic Project}},
address = {{Calgary}},
url = {https://forallx.openlogicproject.org/},
copyright = {All rights reserved},
keywords = {textbook}
}
@article{Matijasevich1992,
title = {My Collaboration with {J}ulia {R}obinson},
author = {Matijasevich, Yuri},
journal = {The Mathematical Intelligencer},
volume = {14},
number = {4},
pages = {38--45},
year = {1992}
}
@book{Menzler-Trott2007,
title = {Logic's Lost Genius: The Life of {G}erhard {G}entzen},
author = {Menzler-Trott, Eckart},
year = 2007,
publisher = {American Mathematical Society},
address = {Providence}
}
@InCollection{Montague1965,
author = {Montague, Richard},
title = {Set theory and higher-order logic},
booktitle = {Formal systems and recursive functions},
publisher = {North-Holland},
year = {1965},
editor = {John {Crossley} and Michael {Dummett}},
pages = {131--48},
address = {Amsterdam},
note = {Proceedings of the Eight Logic Colloquium, July 1963},
}
@book{Noether1983,
title = {Emmy {N}oether: {G}esammelte
{A}bhandlungen---{C}ollected {P}apers},
author = {Jacobson, Nathan},
year = 1983,
publisher = {Springer-Verlag},
address = {Berlin}
}
@misc{Oconnor2014,
author = {O'Connor, John J. and Robertson, Edmund F.},
title = {R\'{o}zsa {P}\'{e}ter},
year = {2014},
url = {http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Peter.html}
}
@misc{Perimeter2015,
author = {Perimeter Institute},
title = {Emmy {N}oether: Her Life, Work, and Influence},
year = 2015,
note = {Video Lecture},
url = {https://www.youtube.com/watch?v=tNNyAyMRsgE}
}
@Article{Peter1935a,
author = {P{\'e}ter, R{\'o}zsa},
title = {{\"U}ber den {Z}usammenhang der verschiedenen
{B}egriffe der rekursiven {F}unktion},
journal = {Mathematische Annalen},
volume = {110},
year = {1935a},
pages = {612--632},
doi = {10.1007/BF01448046}
}
@Article{Peter1935b,
author = {P\'eter, R\'ozsa},
title = {Konstruktion nichtrekursiver {F}unktionen},
journal = {Mathematische Annalen},
volume = 111,
year = {1935b},
pages = {42--60},
doi = {10.1007/BF01472200}
}
@book{Peter1951,
author = {P\'eter, R\'ozsa},
title = {Rekursive Funktionen},
publisher = {Akademiai Kiado},
address = {Budapest},
year = 1951,
note = {English translation in \citep{Peter1967}}
}
@book{Peter1967,
author = {P\'eter, R\'ozsa},
title = {Recursive Functions},
publisher = {Academic Press},
address = {New York},
year = 1967
}
@book{Peter2010,
title = {Playing with Infinity},
author = {P\'eter, R\'ozsa},
year = {2010},
address = {New York},
publisher = {Dover},
url =
{https://books.google.ca/books?id=6V3wNs4uv_4C&lpg=PP1&ots=BkQZaHcR99&lr&pg=PP1#v=onepage&q&f=false}
}
@misc{Radiolab2012,
author = {Radiolab},
title = {The {T}uring Problem},
year = 2012,
note = {Podcast audio},
url =
{http://www.radiolab.org/story/193037-turing-problem/}
}
@misc{RadiolabND,
author = {Radiolab},
title = {{T}alking to Machines},
year = {N.D.},
note = {Podcast audio},
url =
{http://www.radiolab.org/story/137407-talking-to-machines/}
}
@article{Reid1986,
title = {The Autobiography of {J}ulia {R}obinson},
author = {Reid, Constance},
journal = {The College Mathematics Journal},
volume = {17},
issue = {1},
pages = {3--21},
year = {1986}
}
@Book{Reid1996,
author = {Constance Reid},
title = {Julia: A Life in Mathematics},
publisher = {Cambridge University Press},
year = 1996,
address = {Cambridge},
url =
{https://books.google.ca/books?id=lRtSzQyHf9UC&lpg=PP1&pg=PP1#v=onepage&q&f=false}
}
@article{Robinson1949,
URL = {http://www.jstor.org/stable/2266510},
author = {Julia Robinson},
journal = {The Journal of Symbolic Logic},
number = {2},
pages = {98-114},
title = {Definability and Decision Problems in Arithmetic},
volume = {14},
year = {1949}
}
@Book{Robinson1996,
author = {Robinson, Julia},
year = 1996,
title = {The Collected Works of Julia Robinson},
publisher = {American Mathematical Society},
address = {Providence}
}
@misc{Rose2012,
author = {Rose, Daniel},
title = {A Song about {G}eorg {C}antor},
year = 2012,
note = {Audio Recording},
url = {https://www.youtube.com/watch?v=QUP5Z4Fb5k4}
}
@Article{Russell1905,
author = {Bertrand Russell},
title = {On Denoting},
journal = {Mind},
year = 1905,
volume = 14,
pages = {479--493}
}
@book{Russell1967,
author = {Bertrand Russell},
year = 1967,
title = {The Autobiography of Bertrand Russell},
volume = 1,
publisher = {Allen and Unwin},
address = {London}
}
@book{Russell1968,
author = {Bertrand Russell},
year = 1968,
title = {The Autobiography of Bertrand Russell},
volume = 2,
publisher = {Allen and Unwin},
address = {London}
}
@book{Russell1969,
author = {Bertrand Russell},
year = 1969,
title = {The Autobiography of Bertrand Russell},
volume = 3,
publisher = {Allen and Unwin},
address = {London}
}
@book{Russell1983,
author = {Bertrand Russell},
year = 1983,
title = {Collected Papers},
publisher = {Routledge},
address = {London}
}
@misc{RussellND,
author = {Bertrand Russell},
title = {{B}ertrand {R}ussell on Smoking},
year = {n.d.},
note = {Video Interview},
url = {https://www.youtube.com/watch?v=80oLTiVW_lc}
}
@misc{Sautoy2014,
author = {Marcus du Sautoy},
title = {{A} Brief History of Mathematics: {G}eorg {C}antor},
year = 2014,
note = {Audio Recording},
url = {http://www.bbc.co.uk/programmes/b00ss1j0}
}
@book{Segal2014,
title = {Mathematicians under the Nazis},
author = {Segal, Sanford L.},
year = 2014,
publisher = {Princeton University Press},
address = {Princeton}
}
@article{Sigmund2007,
title = {Kurt {G}\"odel: {D}as {A}lbum--{T}he {A}lbum},
author = {Sigmund, Karl and Dawson, John and M\"uhlberger,
Kurt and Enzensberger, Hans Magnus and Kennedy,
Juliette},
journal = {The Mathematical Intelligencer},
volume = 29,
number = 3,
pages = {73--76},
year = 2007,
publisher = {Springer}
}
@book{Smith2013,
title = {An Introduction to G\"odel's Theorems},
author = {Smith, Peter},
year = 2013,
publisher = {Cambridge University Press},
address = {Cambridge}
}
@misc{Society2015,
author = {Beckmann, Arnold and Preining, Norbert},
title = {Kurt {G}\"odel {S}ociety},
year = 2004,
url = {http://kgs.logic.at/index.php?id=2}
}
@inbook{Stalnaker1968,
author = {Stalnaker, Robert C.},
title = {A theory of conditionals},
pages = {98-112},
boobktitle = {Studies in Logical Theory},
editor = {Nicholas Rescher},
publisher = {Basil Blackwell},
address = {Oxford},
year = 1968
}
@misc{Sykes1992,
author = {Sykes, Christopher},
title = {{BBC} {H}orizon: The Strange Life and Death of
{D}r.~{T}uring},
year = 1992,
url = {https://www.youtube.com/watch?v=gyusnGbBSHE}
}
@book{Takeuti2003,
title = {Memoirs of a Proof Theorist: G\"odel and Other
Logicians},
author = {Takeuti, Gaisi and Passell, Nicholas and Yasugi,
Mariko},
year = 2003,
publisher = {World Scientific},
address = {Singapore}
}
@article{Tamassy1994,
title={Interview with {R}\'oza {P}\'eter},
author={Tamassy, Istvan},
journal={Modern Logic},
volume={4},
number={3},
pages={277--280},
year={1994}
}
@book{Tarski1981,
author = {Alfred Tarski},
year = 1981,
title = {The Collected Works of {A}lfred {T}arski},
volume = {I--IV},
publisher = {Birkh\"{a}user},
address = {Basel}
}
@Book{Tarski1983,
author = {John Corcoran},
title = {Logic, Semantics, Metamathematics},
publisher = {Hackett},
year = 1983,
address = {Indianapolis},
edition = {2nd}
}
@misc{Theelen2012,
author = {Theelen, Andre},
title = {LEGO Turing Machine},
year = 2012,
url = {https://www.youtube.com/watch?v=FTSAiF9AHN4}
}
@Article{Turing1937,
author = {Alan M. Turing},
title = {On computable numbers, with an application to the
``{E}ntscheidungsproblem''},
journal = {Proceedings of the London Mathematical Society, 2nd
Series},
year = 1937,
volume = 42,
pages = {230--265}
}
@book{Wang1990,
title = {Reflections on Kurt G{\"{o}}del},
author = {Wang, Hao},
year = 1990,
publisher = {MIT Press},
address = {Cambridge}
}
@Article{Zermelo1904,
author = {Ernst Zermelo},
title = {Beweis, da{\ss} jede {M}enge wohlgeordnet werden
kann},
journal = {Mathe\-ma\-tische An\-nalen},
year = 1904,
volume = 59,
pages = {514--516},
note = {{E}nglish translation in
\cite[pp.~115--119]{Ebbinghaus2010}}
}
@article{Zermelo1908,
title = {Untersuchungen {\"u}ber die {G}rundlagen der
{M}engenlehre~{I}},
author = {Zermelo, Ernst},
journal = {Mathematische Annalen},
volume = 65,
number = 2,
pages = {261--281},
year = 1908,
note = {{E}nglish translation in
\cite[pp.~189-229]{Ebbinghaus2010}}
}
@book{Potter2004,
Author = {Potter, Michael},
Title = {Set Theory and its Philosophy},
Year = {2004},
Address = {Oxford},
Publisher = {Oxford University Press}}
@book{EwaldSieg2013,
Title = {{D}avid {H}ilbert's Lectures on the Foundations of Arithmetic and Logic 1917--1933},
Year = {2013},
Author = {Hilbert, David},
Editor = {Ewald, William Bragg and Sieg, Wilfried},
Address = {Heidelberg},
Publisher = {Springer}}
@book{Berkeley1734,
Year = {1734},
Author = {Berkeley, George},
Title = {The Analyst; or, a Discourse Adressed to an Infidel
Mathematician},
place = {London}
}
@Article{Gouvea2011,
author = {Gouv\^{e}a, Fernando Q.},
title = {Was {C}antor Surprised?},
journal = {American Mathematical Monthly},
year = {2011},
volume = {118},
number = {3},
pages = {198-209}
}
@article{Peano1890,
Author = {Peano, Giuseppe},
Title = {Sur une courbe, qui remplit toute une aire plane},
Journal = {Mathematische Annalen},
Year = {1890},
Volume = {36},
Number = {1},
Pages = {157--60}}
@Article{Boolos1989,
author = {Boolos, George},
title = {Iteration Again},
journal = {Philosophical Topics},
year = {1989},
volume = {17},
number = {2},
pages = {5--21}
}
@Article{Cantor1878,
author = {Cantor, Georg},
title = {Ein {Beitrag} zur {Mannigfaltigkeitslehre}},
journal = {Journal für die reine und angewandte Mathematik},
year = {1878},
volume = {84},
pages = {242--58}
}
@Book{Frege1884,
title = {Die {Grundlagen} der {Arithmetik}: Eine logisch mathematische {Untersuchung} \"{u}ber den {Begriff} der {Zahl}},
publisher = {Wilhelm Koebner},
year = {1884},
author = {Frege, Gottlob},
address = {Breslau},
note = {Translation in \cite{Frege1953}}
}
@book{Frege1953,
address = {Oxford},
edition = {2nd},
title = {Foundations of Arithmetic},
publisher = {Basil Blackwell \& Mott},
author = {Frege, Gottlob},
editor = {J. L. Austin},
year = {1953},
}
@article{BanachTarski1924,
Author = {Banach, Stefan and Tarski, Alfred},
Title = {Sur la d\'{e}composition des ensembles de points en parties respectivement congruentes},
Journal = {Fundamenta Mathematicae},
Volume = {6},
Pages = {244--77},
Year = {1924}}
@misc{Rose2010,
author = {Rose, Nicholas J},
title = {Hilbert-Type Space-Filling Curves},
year = {2010},
url = {https://web.archive.org/web/20151010184939/http://www4.ncsu.edu/~njrose/pdfFiles/HilbertCurve.pdf}
}
@article{KatzKatz2012,
Year = {2012},
Author = {Katz, Karin Usadi and Katz, Mikhail G.},
Title = {{S}tevin Numbers and Reality},
Journal = {Foundations of Science},
Volume = {17},
Number = {2},
Pages = {109--23}}
@incollection{Conway2006,
Author = {Conway, John},
Title = {The Power of Mathematics},
Editor = {Blackwell, Alan and MacKay, David},
Booktitle = {Power},
Series = {Darwin College Lectures},
Publisher = {Cambridge University Press},
Address = {Cambridge},
Year = {2006},
Url = {http://www.cs.toronto.edu/~mackay/conway.pdf}}
@book{Giaquinto2007,
Author = {Giaquinto, Marcus},
Title = {Visual Thinking in Mathematics},
Year = {2007},
Publisher = {Oxford University Press},
Address = {Oxford}}
@Article{Weston2003,
author = {Weston, Tom},
title = {The {Banach}-{Tarski} Paradox},
year = {2003},
url = {http://people.math.umass.edu/~weston/oldpapers/banach.pdf}
}
@Book{Dedekind1888,
title = {Was sind und was sollen die {Zahlen}?},
publisher = {Vieweg},
year = {1888},
author = {Dedekind, Richard},
address = {Braunschweig},
translator = {Ewald, William Bragg},
}
@InCollection{Dedekind1887,
author = {Dedekind, Richard},
title = {\"{A}hnliche (deutliche) {Abbildung} und \"{a}hnliche {Systeme} (11 July 1887)},
booktitle = {Gesammelte mathematische Werke},
publisher = {Friedrich Vieweg \& Sohn},
year = {1932},
pages = {447--449},
address = {Braunschweig}
}
@book{Heijenoort1967,
Author = {Heijenoort, Jean van},
Title = {From {F}rege to {G}\"{o}del: A Source Book in Mathematical Logic, 1879--1931},
Publisher = {Harvard University Press},
Address = {Cambridge, MA},
Year = {1967}}
@book{Kunen1980,
Author = {Kunen, Kenneth},
Title = {Set Theory: An Introduction to Independence Proofs},
Publisher = {North Holland},
Address = {New York},
Year = {1980}}
@article{Boolos1971,
Author = {Boolos, George},
Title = {The Iterative Conception of Set},
Year = {1971},
Journal = {The Journal of Philosophy},
Volume = {68},
Number = {8},
Pages = {215--31}}
@Book{Cohen1966,
title = {Set Theory and the Continuum Hypothesis},
publisher = {Benjamin},
year = {1966},
author = {Cohen, Paul J.},
address = {Reading, MA}
}
@book{Russell1919,
Author = {Russell, Bertrand},
Title = {Introduction to Mathematical Philosophy},
Year = {1919},
Address = {London},
Publisher = {Allen \& Unwin}}
@Article{Hilbert1891,
author = {Hilbert, David},
title = {\"{U}ber die stetige {Abbildung} einer {Linie} auf ein {Fl\"{a}chenst\"{u}ck}},
journal = {Mathematische Annalen},
year = {1891},
volume = {38},
number = {3},
pages = {459--460}
}
@article{Zermelo1908Untersuchungen,
Author = {Zermelo, Ernst},
Title = {Untersuchungen \"{u}ber die {G}rundlagen der {M}engenlehre {I}},
Journal = {Mathematische Annalen},
Year = {1908},
Volume = {65},
Pages = {261--81}}
@article{Hartogs1915,
Author = {Hartogs, Friedrich},
Title = {\"{U}ber das {P}roblem der {W}ohlordnung},
Journal = {Mathematische Annalen},
Year = {1915},
Volume = {76},
Pages = {438--43}}
@book{Vitali1905,
author = {Vitali, Giuseppe},
title = {Sul problema della misura dei gruppi di punti di una retta},
publisher = {Gamberini e Parmeggiani},
year = {1905},
address = {Bologna}
}
@Book{WhiteheadRussell1910,
title = {Principia Mathematica},
publisher = {Cambridge University Press},
year = {1910},
author = {Whitehead, Alfred North and Russell, Bertrand},
volume = {1},
address = {Cambridge}
}
@article{Ramsey1925,
Author = {Ramsey, Frank Plumpton},
Title = {The Foundations of Mathematics},
journal = {Proceedings of the London Mathematical Society},
Year = {1925},
volume = {25},
pages = {338--384}
}
@Article{Linnebo2010,
author = {Linnebo, \O{}ystein},
title = {Predicative and Impredicative Definitions},
journal = {Internet Encyclopedia of Philosophy},
year = {2010},
lastchecked = {15 Oct 2014},
url = {http://www.iep.utm.edu/predicat/}
}
@Article{VonNeumann1925,
author = {von Neumann, John},
title = {Eine {Axiomatisierung} der {Mengenlehre}},
journal = {Journal f\"{u}r die reine und angewandte {Mathematik}},
year = {1925},
volume = {154},
pages = {219--40}
}
@Article{Benacerraf1965,
author = {Benacerraf, Paul},
title = {What numbers could not be},
journal = {The Philosophical Review},
year = {1965},
volume = {74},
number = {1},
pages = {47--73}
}
@InCollection{Montague1961,
author = {Montague, Richard},
title = {Semantic closure and non-finite axiomatizability {I}},
booktitle = {Infinitistic Methods: Proceedings of the Symposium on Foundations of Mathematics (Warsaw 1959)},
publisher = {Pergamon},
year = {1961},
pages = {45--69},
address = {New York}
}
@Article{Burali-Forti1897,
author = {Burali-Forti, Cesare},
title = {Una questione sui numeri transfiniti},
journal = {Rendiconti del Circolo Matematico di Palermo},
year = {1897},
volume = {11},
pages = {154--64}
}
@Book{Cantor1883,
title = {Grundlagen einer allgemeinen {Mannigfaltigkeitslehre}. Ein mathematisch-philosophischer {Versuch} in der {Lehre} des {Unendlichen}},
publisher = {Teubner},
year = {1883},
author = {Cantor, Georg},
address = {Leipzig}
}
@Book{Incurvati2020,
Author = {Incurvati, Luca},
Title = {Conceptions of Set and the Foundations of Mathematics},
Year = {2020},
Address = {Cambridge},
Publisher = {Cambridge University Press}}
@phdthesis{IncurvatiThesis,
Author = {Incurvati, Luca},
Title = {Set {T}heory: Its {J}ustification, {L}ogic, and {E}xtent},
Year = {2010},
School = {Cambridge University}}
@Article{OConnorRobertson:RN,
author = {O'Connor, John J. and Robertson, Edmund F.},
title = {The real numbers: {Stevin} to {Hilbert}},
year = {2005},
url = {http://www-history.mcs.st-and.ac.uk/HistTopics/Real_numbers_2.html},
}
@InCollection{Shoenfield:AST,
author = {Shoenfield, Joseph R.},
title = {Axioms of Set Theory},
booktitle = {Handbook of Mathematical Logic},
publisher = {North-Holland},
year = {1977},
editor = {Jon Barwise},
pages = {321--44},
address = {London}
}
@Article{Cantor1892,
author = {Cantor, Georg},
title = {{\"Uber} eine elementare {Frage} der {Mannigfaltigkeitslehre}},
journal = {Jahresbericht der deutschen Mathematiker-Vereinigung},
year = {1892},
volume = {1},
pages = {75--8},
address = {Leipzig},
publisher = {Teubner}
}
@Book{Hume1740,
title = {A Treatise of Human Nature},
year = {1740},
author = {Hume, David},
address = {London}
}
@InCollection{Scott1974,
author = {Scott, Dana},
title = {Axiomatizing Set Theory},
booktitle = {Axiomatic Set Theory II},
publisher = {American Mathematical Society},
year = {1974},
editor = {Thomas Jech},
pages = {207--14},
note = {Proceedings of the Symposium in
Pure Mathematics of the American Mathematical Society, July--August 1967}
}
@InCollection{Boolos2000,
author = {Boolos, George},
title = {Must we Believe in Set Theory?},
booktitle = {Between Logic and Intuition: Essays in Honor of {Charles} {Parsons}},
publisher = {Cambridge University Press},
year = {2000},
editor = {Gila {Sher} and Richard {Tieszen}},
pages = {257--68},
address = {Cambridge}
}
@Article{FefermanLevy1963,
author = {Solomon {Feferman} and Azriel {Levy}},
title = {Independence results in set theory by {Cohen}'s method {II}},
journal = {Notices of the American Mathematical Society},
year = {1963},
volume = {10},
pages = {593}
}
@Article{Cohen1963,
author = {Cohen, Paul J.},
title = {The independence of the continuum hypothesis},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {1963},
volume = {24},
pages = {556--557}
}
@Article{Godel1938,
author = {G\"odel, Kurt},
title = {The consistency of the axiom of choice and the generalized continuum hypothesis},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {1938},
volume = {50},
pages = {1143--8}
}
@Article{Fraenkel1922,
author = {Fraenkel, Abraham},
title = {\"{U}ber den {Begriff} `definit' und die {Unabh\"angigkeit} des {Auswahlaxioms}},
journal = {Sitzungsberichte der Preussischen Akadademie der Wissenschaften, Physikalisch-mathematische Klasse},
year = {1922},
pages = {253--257}
}
@inproceedings{Skolem1922,
author = {Skolem, Thoralf},
title = {Einige {Bemerkungen} zur axiomatischen {Begr\"undung} der {Mengenlehre}},
booktitle = {Wissenschaftliche Vortr\"age gehalten auf dem f\"unften
Kongress der skandanivschen Mathematiker in Helsingfors vom 4.\ bis
zum 7.\ Juli 1922},
place = {Helsinki},
publisher = {Akademiska Bokhandeln},
year = {1922},
pages = {137--52}
}
@Book{Wagon2016,
title = {The {Banach}-{Tarski} Paradox},
publisher = {Cambridge University Press},
year = {2016},
author = {Grzegorz {Tomkowicz} and Stan {Wagon}},
address = {Cambridge}
}
@Article{Hausdorff1914,
author = {Hausdorff, Felix},
title = {Bemerkung über den {Inhalt} von {Punktmengen}},
journal = {Mathematische Annalen},
year = {1914},
volume = {75},
pages = {428--34}
}
@Article{Robinson1947,
author = {Robinson, Raphael},
title = {On the decomposition of spheres},
journal = {Fundamenta Mathematicae},
year = {1947},
volume = {34},
number = {1},
pages = {246--60}
}
@Article{Levy1960,
author = {L\'{e}vy, Azriel},
title = {Axiom Schemata of Strong Infinity in Axiomatic Set Theory},
journal = {Pacific Journal of Mathematics},
year = {1960},
volume = {10},
number = {1},
pages = {223--38}
}
@book{Solow2013,
author = {Daniel Solow},
year = {2013},
title = {How to Read and Do Proofs},
publisher = {Wiley},
address = {Hoboken, NJ}
}
@book{Velleman2019,
author = {Daniel J. Velleman},
title = {How to Prove It: A Structured Approach},
year = {2019},
edition = {3rd},
publisher = {Cambridge University Press},
address = {Cambridge}
}
@book{Hammack2013,
author = {Richard Hammack},
title = {Book of Proof},
year = {2013},
publisher = {Virginia Commonwealth University},
address = {Richmond, VA},
url =
{http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf}
}
@book{Sandstrum2019,
author = {Ted Sandstrum},
year = {2019},
title = {Mathematical Reasoning: Writing and Proof},
publisher = {Grand Valley State University},
address = {Allendale, MI},
url = {https://scholarworks.gvsu.edu/books/7/}
}
@book{Steinhart2018,
author = {Eric Steinhart},
year = {2018},
title = {More Precisely: The Math You Need to Do Philosophy},
publisher = {Broadview},
address = {Peterborough, ON},
edition = {2nd}
}
@misc{Hutchings2003,
author = {Michael Hutchings},
title = {Introduction to Mathematical Arguments},
year = {2003},
url = {https://math.berkeley.edu/~hutching/teach/proofs.pdf}
}
@misc{Cheng2004,
author = {Eugenia Cheng},
title = {How to Write Proofs: A Quick Quide},
year = {2004},
url = {https://eugeniacheng.com/wp-content/uploads/2017/02/cheng-proofguide.pdf}
}
@book{Smullyan1968,
author = {Smullyan, Raymond M.},
publisher = {Springer},
address = {New York, NY},
title = {First-Order Logic},
year = {1968},
note = {Corrected reprint, New York, NY: Dover, 1995}
}
@book{Smullyan1995,
author = {Smullyan, Raymond M.},
publisher = {Dover},
address = {Mineola, NY},
title = {First-Order Logic},
year = {1995},
note = {Corrected reprint of \citet{Smullyan1968}}
}
@article{Zuckerman1973,
author = {Zuckerman, Martin M.},
journal = {Notre Dame Journal of Formal Logic},
number = {1},
pages = {134--138},
title = {Formation sequences for propositional formulas},
volume = {14},
year = {1973}}